On a simple level, a digital system is just one that works with discrete states. Digital computers are designed around electrical circuitry that has just two states: fully on and fully off. We typically associate these states with the binary values 1 and 0. Once you have such a setup, you can easily represent richer values - such as the price of a plane ticket - by using the state of a group of on/off memory circuits.
However,
all digital systems are physical. If we take physical nature to be essentially
analog,
then we need to say that all digital systems are also analog.
So, to be digital is really a design choice, not unlike the choice one would make between clockwork and hydraulics when deciding how to achieve a specific task.
What
distinguishes digital systems from all others is that they are designed to
reliably interpret analog properties in discrete ways. For example, a
bit of memory in a digital system will only be read as on or off by the
reading circuitry because of its electrical design.
However, the memory circuit itself will have variable analog electrical
characteristics since its a physical/analog device - a bit like a battery.
Some see digital systems as special since they deal intimately with pure information and absolute states, and wonder if this could mean they are somehow connected to the divine. If this is the case, digital systems might be a place where we would expect to see divine activity. However, since digital systems are designed to operate in a thoroughly deterministic, reliable - even fault-tolerant manner - they are probably the last place we should expect to see such activity.
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